Using genetic algorithm for solving quadratic bilevel programming problems via fuzzy goal programming

This article presents how genetic algorithm (GA) can be efficiently used to fuzzy goal programming (FGP) formulation of quadratic bilevel programming problems (QBLPPs) in a hierarchical decision system. In the proposed approach, the concept of tolerance membership functions in fuzzy sets for measuring the achievement of highest membership value (unity) of the defined fuzzy goals of a problem to the extent possible by minimising the under-deviational variables of the defined membership goals on the basis of priorities of achieving the fuzzy goals is considered. In the decision making process, the sensitivity analysis with variations of priority structure of the goals is performed and then the notion of Euclidean distance function is used to identify the appropriate priority structure under which the most satisfactory decision can be reached in the fuzzy decision environment. The potential use of the approach is illustrated by a numerical example.